Online sports betting is growing rapidly around the world. We describe how the competitive structure of the bookmaking market affects odds when bettors disagree about the probabilities of the outcomes of sporting events but are on average correct. We show that the demand for bets on longshots is less sensitive to the odds than bets on favorites. This means monopolistic bookmakers will set odds exhibiting favorite-longshot bias while competitive bookmaking markets will not have this feature. We develop a version of the model for soccer matches and use these results to explain empirical findings on odds for over 80,000 European soccer games from two different bookmaking markets.